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Exponents/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby. Tim and Moby are dressed in white uniforms. Tim is piloting a submarine through a human bloodstream. TIM: I knew we should have turned left at the last artery. Moby beeps. TIM: I will turn this submarine around, mister! A letter appears. Text reads as Tim narrates: Dear Tim and Moby, How do I use exponents? From, Clare TIM: Thanks to Moby's shrinking machine and my bad sense of direction, it looks like we're stuck here for a while. So let's talk exponents! An exponent is just another way to show repeated multiplication. A label appears, reading, exponent. A variable, X, appears, with a smaller variable, Y, above it to the right. TIM: Take the number 125. We can get this number by multiplying the number 5 by itself 3 times, so let's write it as a product of its factors: 5 times 5 times 5. An equation appears, reading, 5 times 5 times 5 equals 125. TIM: 125 is what we call standard form. A label appears, reading, standard form. TIM: In exponential form, it would be 5 raised to the third power. On-screen, the number, 5, appears, with a smaller number, 3, above it to the right. TIM: 5 is our base number, and 3 is our exponent, which basically tells us how many times our base is being multiplied by itself. Moby beeps. TIM: Sure they're useful! Especially for… On-screen, a wave of white blood cells swarm past the submarine. TIM: Whoa! Moby beeps. TIM: Yeah, that was pretty intense! How many white blood cells do you think were in that wave? Let's check the ship's sensors. On-screen, Tim consults the computer. Text on the screen reads, White Blood Cells Detected: 16,384. TIM: Ah, good, this will illustrate my point perfectly! Like I was saying, exponents are useful for writing numbers that are really big or really small. 16,384 is a pretty big number, and sort of a mouthful to say! It just so happens that we can rewrite it in exponent form as 2 to the 14th power. On-screen, a number appears, reading, 2 to the 14th power. TIM: If you multiply 2 times 2, times 2, times 2, times 2, times 2… and so on up to 14 2's, you end up with 16,384! An equation appears, with 14 2's, multiplied to equal 16,384. Moby beeps. TIM: Right, well those are positive exponents, since they deal with positive numbers. A label appears, reading, positive exponents. TIM: There are also negative exponents. A label appears, reading, negative exponents. TIM: It's exactly what it sounds like: an exponent that's a negative number. While positive exponents give us really big numbers, negative exponents give us very small numbers. Let’s take the distance we've traveled along the blood vessels of this body. On-screen, Tim consults the computer. Text on the screen reads, distance traveled: 8 millimeters. TIM: Although it seems like we've been trapped in this sub forever, we've really only traveled a grand total of 8 millimeters. Moby beeps. TIM: Well, what do you expect? We're microscopic! Millimeters are pretty small, so let's convert our distance traveled to a unit we're more used to dealing with: meters. There are 1,000 millimeters in a meter, so 8 millimeters is equal to 8 one-thousandth of a meter, or 1 one-twenty-fifth. An equation appears, reading, 8 times 1 one-thousandth equals 8 one-thousandth, equals 1 one-twenty-fifth. TIM: Okay, remember how we said the exponent form of 125 is 5 to the third power? That means we can rewrite 1 one-twenty-fifth as 1 over 5 to the third power. An equation appears, reading, 1 over 125 equals 1 over 5 to the third power. TIM: And here's the really neat part: a positive exponent in the denominator of a fraction is actually the same as a negative exponent, only with the base in the numerator! Which means 1 over 5 to the third power equals 5 to the negative third power. An equation appears, reading, 1 over 5 to the third power equals 5 to the negative third power. TIM: So all you need to do to switch between positive and negative exponents is to take the reciprocal of the base! Moby beeps. TIM: Good point. With really really big or really really small numbers, it's probably a good idea to use scientific notation, a way of writing numbers that raises factors of 10 to different powers. A label appears, reading, scientific notation. Two equations appear: 1,000,000 equals 1 times 10 to the sixth power, and 1 one-millionth equals 1 times 10 to the negative sixth power. TIM: Check out the Scientific Notation movie for more on that when you get a chance, but for right now, let's grab this red blood cell. On-screen, a claw from the submarine captures a passing red blood cell. Tim consults the computer. Text on the screen reads, red blood cells per cubic millimeter: 5,000,000. TIM: According to the ship's database, the average human body has about 5 million red blood cells per cubic millimeter of blood! Instead of writing out that huge number as 5 plus 6 0's, we can convert it to scientific notation. An equation appears, reading, 5,000,000 equals 5 times 10 to the sixth power. TIM: Care to guess how big each red blood cell is? Moby beeps. TIM: The average red blood cell has a diameter of 7 microns, which is equivalent to 7 one-millionths of a meter! We can convert that to scientific notation, too. An equation appears, reading, 7 one-millionths equals 7 times 10 to the negative sixth power. TIM: See, it's much easier without all those 0's! Now, if we could only find our way out of this body… Moby beeps. The submarine approaches a sign with an arrow that reads, kidneys: 0.6 meters. TIM: This ought to be interesting… Category:BrainPOP Transcripts